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We make this statement falsifiable. The \\emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier fed by seven executable rule-derived audits reaches $1.00$ classification accuracy. In three matched $100$-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ leg","title":"Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models","url":"https://arxiv.org/abs/2606.29091","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.29091v1 Announce Type: cross \nAbstract: Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them. We make this statement falsifiable. The \\emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier fed by seven executable rule-derived audits reaches $1.00$ classification accuracy. In three matched $100$-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ leg","title":"Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-30T04:43:04Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.29091"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0585e756392366026e145420bfb3e2a10d34d7f00722c29a5ea9234cafe9e67c5c833215941c30ace29f8a3c0ee51bf1af5df6b3425e3228e21036c21d63e100","signer":"crovia.substrate","subject":{"observed_at":"2026-06-30T04:43:04Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.29091"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"ff9a719e1a9ea4d6d96c157417472b58dd590e009b3cd259ba69ec9ac8eeba0a","leaf_index":264860,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"ce794e3ac40e69fb7415c0008a9ada78a047589e1e8c0da6d1e17363d2a1beb8","side":"right"},{"sibling":"5866e2a98fe89e68f2f9884fec7b8aaa5ca0014a577018376dc2216fc32a9ccd","side":"right"},{"sibling":"f4892774d9bc98487d71d0c0b215066bace046d35cdd64bff2a0e6148862a8db","side":"left"},{"sibling":"e47cafe1c2f42fd05e6f338dc858064a5eba22c3f8fb239d99b122c121618b4a","side":"left"},{"sibling":"d09e5cd545c7724aceb8f9cd56ac32a1350ebec6e837d965ff60f65e3d135d34","side":"left"},{"sibling":"21aeb247f596e755f92e03c02397140679f193fb3b000cc11078505b42970abc","side":"right"},{"sibling":"07528e32fda4a58ff6ab8ca2268cc78d4ff4ed66bfadde9432f593a2fb4e74e7","side":"right"},{"sibling":"86ba07f5dfcbf22e044b5aa0ecc15cd2f29de9218e54da603c4ffe753c522516","side":"left"},{"sibling":"5767f14b55df4212d25ae2f52b8f3d4abff2555c65ba62935ed6cb0a8e617b43","side":"right"},{"sibling":"1549a8883ab3267f958dc2624919e40c65c82958b8005967ed6a4da1247da0ad","side":"left"},{"sibling":"23994bf0974e5c9c7f63a61b4f0a48b0ca756a4adc34a8f85f878e774c37dfbe","side":"right"},{"sibling":"f9b4bed84fa6990c71ad2887c91bda183001f05f6b648f21d1273045a26b11fd","side":"left"},{"sibling":"173d2dc4b29ee04ea41d6d0ebc334c4bc2d46e7ee4230c94765413f24fb4bc42","side":"right"},{"sibling":"112461f7c0ec411116fb5c6c90fe95cea9d8f188b9fe08afe25a837ac02d0071","side":"right"},{"sibling":"ea9488204352c49db8f7daf05eefcd7628ecf9413830346674801a99d0654a94","side":"right"},{"sibling":"6261c13b9922cb657f10d1e5d36ec15d8771cf8766e36c61dcbffb7bed57e396","side":"right"},{"sibling":"fa19aa3faf287618b820bcfceebb366152ad521dd20ef9f51e977816663e448b","side":"right"},{"sibling":"c32f943406b62d1fc59b7f7e243492174c8e1caba8c8a2705f86c773315736e0","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":265374,"merkle_root":"9636001ecab173cb6af10dc7c71eb14585daa62f9c0a6f027046f05633156891","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260630T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-30T05:38:03Z","sig_algorithm":"ed25519","signature":"6d4b8fd9b9da856cbb5fba7540877c6a63fa18a5ec3eaf28dc4d6d1c64921c9c0565f8c95f4b7aec0e7744fd7754844f051baf863db708cad768765b416a7b0c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_90dd517dc0204adc3ddd61cadfd2f1bfee08bba23d38f6065afb8d9376895ef7"}}